In order to improve the efficiency of the slice sampler, [1]}
proposed to sample in a block \(u\)  and \(w\)  and to rewrite the joint
density (REF ) as
\(f_{\mathbf {\varepsilon },u,l}\left(\mathbf {\varepsilon },u,l\right)=\mathbb {I}\left(\xi _{l}>u\right)\frac{w_{l}}{\xi _{l}}\text{logN}_{d}\left(\mathbf {\varepsilon }\left|\mathbf {m}_{l},\mathbf {\Sigma }_{l}\right.\right),\) 
